Solving

 HAPPY HALLOWEEN!                                                                                                                      

  Easier problem:

Asked Chatgpt/Bing to solve it 'cold'.

                                                                  

https://www.mathcha.io/

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Bard's solution:

There are two ways to solve the quadratic equation 9x^2 + 6x + 1 = 0:

Method 1: Factoring

We can factor the quadratic as follows:

9x^2 + 6x + 1 = (3x + 1)^2

Setting each factor equal to zero, we get:

3x + 1 = 0

Solving for x, we get:

x = -1/3

Therefore, the solution to the quadratic equation is x = -1/3.

Method 2: Using the Quadratic Formula

The quadratic formula can be used to solve any quadratic equation, regardless of whether it can be factored. The quadratic formula is:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 9, b = 6, and c = 1. Substituting these values into the quadratic formula, we get:

x = (-6 ± √(6² - 4 * 9 * 1)) / 2 * 9

Simplifying, we get:

x = (-6 ± √0) / 18

Since the square root of zero is zero, we can simplify further to get:

x = (-6 ± 0) / 18

Therefore, the solution to the quadratic equation is x = -1/3.

Both methods give us the same solution.

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Bard code that works for generating true quadratics:

                                                                                        

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